On the Hölder Property of Solutions of a Generalized System of Beltrami Equations

Abstract

We define a generalized Beltrami system, which is a broad generalization of the scalar Beltrami equation to vector equations. The Riemann-Hilbert boundary value problem is considered for such a system under the assumption that it is elliptic (i.e., the roots of the characteristic equation belong to the interior of the unit disk centered at zero). A Cordes type condition on the location of the roots of the characteristic equation of the system is obtained; this is a sufficient condition for the solution of this problem to have the Hölder property. The proof is based on the properties of singular integral operators in a domain.